Application of Polynomial Approximation to Estimate the RMS Measurement Error of the Polyharmonic Signal Caused by ADC Nonlinearity

At present, the shape of the signals of real electrical power grids are very different from the sinusoidal: noise, flicker and non-fundamental harmonics take place. To measure such signals, digital methods are applied, among which a group of methods based on the approximation of signal samples can be distinguished. One of the most significant components of the error is the error caused by the ADC nonlinearity. Currently, the effective methods for estimating this error does not exist. The paper proposes an approach based on the application of second and third order polynomials to estimate this error. Expressions are obtained for estimating the RMS measurement error for a signal of arbitrary spectral composition. The evaluation of the proposed approach with the “worst case” method is carried out. By the application of Simulink software, a simulation model was performed that allows to check the obtained analytical expressions. It is shown that the application of an approximating third-order polynomial characterizes a significantly higher error estimate than for a second-order polynomial.